Maybe a sea witch could be the main antagonist. She could be using her magic to cause trouble for Percy and Annabeth. She might be trying to stop them from finding a certain treasure because it has the power to break her spells. The sea witch could send all kinds of sea creatures and illusions to thwart their plans.
The main antagonists could be other pirate crews. There might be a particularly ruthless pirate captain who wants to take over Percy and Annabeth's ship and all the treasures they might be after. This captain could be jealous of Percy's powers and see him as a threat.
Well, perhaps the fanfic could start with Percy and Annabeth being magically transported into a world of pirates. They are initially confused but quickly realize they need to work together. Percy might be a natural at sword - fighting on the ship, while Annabeth tries to figure out the politics among the different pirate crews. They could be on a quest to find a magical artifact that the pirates believe will give them ultimate power over the seas.
It could be the navy. They see pirates as outlaws and would be determined to capture Percy and his crew. They might have better - equipped ships and more trained soldiers, making them a formidable foe for Percy and his fellow pirates.
The Titans could be antagonists. Even though they have been defeated before, some of them might hold a grudge against Percy and Annabeth and see their baby as a new target for revenge. They could try to kidnap the baby to use it as a bargaining chip or to corrupt it to their side.
It could be an old enemy from Greek mythology that has been resurrected. For example, a powerful Titan who has a vendetta against the demigods, especially Percy and Annabeth.
Often, it could be old enemies like the Titans. In fanfiction, they might return in new and more devious ways. For example, Kronos could have a new plan to break Percy and Annabeth apart before trying to take over the world again.
Often, it could be a jealous classmate. Maybe someone who has a crush on Percy and sees Annabeth as a threat, so they try to create problems between them. Another could be a strict teacher who doesn't like Percy's carefree attitude and Annabeth's independent thinking, always trying to give them a hard time.
The Titans could still be antagonists. In the Percy Jackson universe, they are powerful and malevolent. A princess in a fanfic might have to face their wrath as they try to overthrow the gods and take over the world. They would see the princess as a threat, especially if she is allied with the gods or has some special power that could stop them.
The main antagonists in a 'Percy back in time fanfic' could be the followers of the Titans. They were numerous and loyal to Kronos. They would view Percy as an enemy since he is from a time when the Olympians are in power. Additionally, if Percy travels to a time when a powerful and evil demigod once lived, that demigod could be an antagonist. For example, if he goes back to a time when a demigod was on a path of destruction before being stopped, Percy's arrival might disrupt the events that were supposed to stop that demigod, and so the demigod would turn against Percy. There's also the possibility of some ancient sea monsters that were more prevalent in the past and were under the control of the Titans or other evil forces.
The Titans could still be antagonists. Since Percy has a connection to Hecate, they might see him as a threat to their plans of overthrowing the gods. They could try to capture him to use his powers for their own evil purposes.
One potential main antagonist could be a powerful pirate captain who sees Harry as a threat to his control over the seas. Maybe this captain has some dark magic powers as well.